Decentralized Recommendations Using Distributed Average Consensus

2. The method of claim 1, wherein the user preference data is a user preference vector, wherein each element in the user preference vector corresponds to an item of the set of items, and wherein sampling the user preference data comprises calculating a sampled user preference matrix by multiplying a random matrix and the user preference vector.

3. The method of claim 2, wherein the consensus result is a global consensus matrix of a same dimensionality as the sampled user preference matrix, and wherein determining the recommendation model based on the consensus result for the sampled user preference data comprises extracting the recommendation model from the global consensus matrix using orthogonal decomposition.

7. The method of claim 6, wherein, after a plurality of iterations, the consensus sampled user preference data calculated by the distributed computing device substantially converges with consensus sampled user preference data calculated by each of remaining ones of the plurality of additional computing devices, and the consensus sampled user preference data calculated by the distributed computing device is the consensus result.

8. The method of claim 5, wherein sampling the user preference data obscures the user preference data, such that the second distributed computing device cannot recover the user preference data from the sampled user preference data.

10. The method of claim 9, wherein determining whether the consensus result has been obtained based on the updated first convergence indicator comprises determining that the first convergence indicator of the distributed computing device is within a threshold distance of a global center of mass of the first convergence indicator.

12. The non-transitory computer-readable medium of claim 11, wherein the user preference data is a user preference vector, wherein each element in the user preference vector corresponds to an item of the set of items, and wherein the instructions to sample the user preference data comprise instructions to calculating a sampled user preference matrix by multiplying a random matrix and the user preference vector.

13. The non-transitory computer-readable medium of claim 12, wherein the consensus result is a global consensus matrix of a same dimensionality as the sampled user preference matrix, and wherein the instructions to determine the recommendation model based on the consensus result for the sampled user preference data comprise instructions to extract the recommendation model from the global consensus matrix using orthogonal decomposition.

17. The non-transitory computer-readable medium of claim 16, wherein, after a plurality of iterations, the consensus sampled user preference data calculated by the distributed computing device substantially converges with consensus sampled user preference data calculated by each of remaining ones of the plurality of additional computing devices, and the consensus sampled user preference data calculated by the distributed computing device is the consensus result.

18. The non-transitory computer-readable medium of claim 15, wherein the sampling of the user preference data obscures the user preference data, such that the second distributed computing device cannot recover the user preference data from the sampled user preference data.

20. The non-transitory computer-readable medium of claim 19, wherein the instructions to determine whether the consensus result has been obtained based on the updated first convergence indicator comprise instructions to determine that the first convergence indicator is within a threshold distance of a global center of mass of the first convergence indicator.